14x^2-6x=2x+4

Solution for 14x^2-6x=2x+4 equation:

Simplifying
14x2 + -6x = 2x + 4

Reorder the terms:
-6x + 14x2 = 2x + 4

Reorder the terms:
-6x + 14x2 = 4 + 2x

Solving
-6x + 14x2 = 4 + 2x

Solving for variable 'x'.

Reorder the terms:
-4 + -6x + -2x + 14x2 = 4 + 2x + -4 + -2x

Combine like terms: -6x + -2x = -8x
-4 + -8x + 14x2 = 4 + 2x + -4 + -2x

Reorder the terms:
-4 + -8x + 14x2 = 4 + -4 + 2x + -2x

Combine like terms: 4 + -4 = 0
-4 + -8x + 14x2 = 0 + 2x + -2x
-4 + -8x + 14x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-4 + -8x + 14x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -4x + 7x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-2 + -4x + 7x2)' equal to zero and attempt to solve:

Simplifying
-2 + -4x + 7x2 = 0

Solving
-2 + -4x + 7x2 = 0

Begin completing the square.  Divide all terms by
7 the coefficient of the squared term: 

Divide each side by '7'.
-0.2857142857 + -0.5714285714x + x2 = 0

Move the constant term to the right:

Add '0.2857142857' to each side of the equation.
-0.2857142857 + -0.5714285714x + 0.2857142857 + x2 = 0 + 0.2857142857

Reorder the terms:
-0.2857142857 + 0.2857142857 + -0.5714285714x + x2 = 0 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + -0.5714285714x + x2 = 0 + 0.2857142857
-0.5714285714x + x2 = 0 + 0.2857142857

Combine like terms: 0 + 0.2857142857 = 0.2857142857
-0.5714285714x + x2 = 0.2857142857

The x term is -0.5714285714x.  Take half its coefficient (-0.2857142857).
Square it (0.08163265305) and add it to both sides.

Add '0.08163265305' to each side of the equation.
-0.5714285714x + 0.08163265305 + x2 = 0.2857142857 + 0.08163265305

Reorder the terms:
0.08163265305 + -0.5714285714x + x2 = 0.2857142857 + 0.08163265305

Combine like terms: 0.2857142857 + 0.08163265305 = 0.36734693875
0.08163265305 + -0.5714285714x + x2 = 0.36734693875

Factor a perfect square on the left side:
(x + -0.2857142857)(x + -0.2857142857) = 0.36734693875

Calculate the square root of the right side: 0.606091527

Break this problem into two subproblems by setting 
(x + -0.2857142857) equal to 0.606091527 and -0.606091527.

Subproblem 1
x + -0.2857142857 = 0.606091527

Simplifying
x + -0.2857142857 = 0.606091527

Reorder the terms:
-0.2857142857 + x = 0.606091527

Solving
-0.2857142857 + x = 0.606091527

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.2857142857' to each side of the equation.
-0.2857142857 + 0.2857142857 + x = 0.606091527 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + x = 0.606091527 + 0.2857142857
x = 0.606091527 + 0.2857142857

Combine like terms: 0.606091527 + 0.2857142857 = 0.8918058127
x = 0.8918058127

Simplifying
x = 0.8918058127

Subproblem 2
x + -0.2857142857 = -0.606091527

Simplifying
x + -0.2857142857 = -0.606091527

Reorder the terms:
-0.2857142857 + x = -0.606091527

Solving
-0.2857142857 + x = -0.606091527

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.2857142857' to each side of the equation.
-0.2857142857 + 0.2857142857 + x = -0.606091527 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + x = -0.606091527 + 0.2857142857
x = -0.606091527 + 0.2857142857

Combine like terms: -0.606091527 + 0.2857142857 = -0.3203772413
x = -0.3203772413

Simplifying
x = -0.3203772413

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.8918058127, -0.3203772413}
Solution
x = {0.8918058127, -0.3203772413}